TY  - JOUR
N2  - We consider continuous-time diffusion models driven by fractional Brownian motion.
Observations are assumed to possess a nontrivial likelihood given the latent path. Due to the
non-Markovian and high-dimensional nature of the latent path, estimating posterior expectations
is computationally challenging. We present a reparameterization framework based on the
Davies and Harte method for sampling stationary Gaussian processes and use it to construct a
Markov chain Monte Carlo algorithm that allows computationally efficient Bayesian inference.
The algorithm is based on a version of hybrid Monte Carlo simulation that delivers increased
efficiency when used on the high-dimensional latent variables arising in this context. We specify
the methodology on a stochastic volatility model, allowing for memory in the volatility increments
through a fractional specification. The method is demonstrated on simulated data and on
the S&P 500/VIX time series. In the latter case, the posterior distribution favours values of the
Hurst parameter smaller than 1/2, pointing towards medium-range dependence.
ID  - discovery1474799
KW  - Bayesian inference
KW  -  Davies and Harte algorithm
KW  -  Fractional Brownian motion
KW  -  Hybrid Monte Carlo algorithm
TI  - Bayesian inference for partially observed stochastic differential equations driven by fractional Brownian motion
AV  - public
Y1  - 2015/12//
EP  - 827
UR  - http://dx.doi.org/10.1093/biomet/asv051
SN  - 0006-3444
JF  - Biometrika
A1  - Beskos, A
A1  - Dureau, J
A1  - Kalogeropoulos, K
VL  - 102
SP  - 809
IS  - 4
N1  - © 2015 Biometrika Trust. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/
licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
ER  -